Can I specify a portion of the image to render in Cycles?
You can use border render, like explained in the wiki :


  You can render just a portion of the view instead of rendering the entire frame. While in Camera View, enable Border and press CtrlB, then drag a rectangle to define the area you want to render. CtrlAltB is the shortcut to disable the border. 
      Note that this disables the Save Buffers option in Performance and Full Sample option in Anti-Aliasing. 
  
  Enabling Crop will crop the rendered image to the Border size, instead of rendering a black region around it.




This answer goes further in explaining this feature.

If needed, you can set the border position with python, for instance :

bpy.data.scenes["Scene"].render.use_border = True      # Tell Blender to use border render
bpy.data.scenes["Scene"].render.border_max_y = 0.75    # Set the border top at 3/4 of the image's height
bpy.data.scenes["Scene"].render.border_min_y = 0.33    # Set the border bottom at 1/3 of the image's height
bpy.data.scenes["Scene"].render.border_min_x = 0.25    # Set the border left at 1/4 of the image's width
bpy.data.scenes["Scene"].render.border_max_x = 1.0     # Set the border right at the image's right border


And then, just hit render !